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Proof step 13 from proof recovery (previous step)

# lpt0 = # avol0 - sb.main, sb.main + # lpt4 = # avol0, avol0[sb.log] = mapped(buf1), avol0[sb.orph] = mapped(buf0), avol0[0] = mapped(buf), adr1 = adr2, avol4 = avol1, log1 = log2, lpt1 = lpt2, m4 = m5, orphans = ns1, disk-layout(sb, # lpt4), ebm-vol-inv(subarray(avol0, sb.main, # lpt0)), ebm-vol-inv(avol0), is-encoded(sb, buf), is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log0, buf1), is-encoded(lpt4, lebs(avol0, sb.lpt, lptlebs(# lpt4, LEB_SIZE))), is-encoded-pad(ns0, sb.orphsize, buf0), mapped-full?(avol0, sb.lpt, lptlebs(# lpt4, LEB_SIZE)), avol0 ⊆ avol1, m1 ≠ LEB_SIZE → # buf1 = m1 ⊦ [persistence_io_recover#(; adr1, m4, orphans, log1, lpt1, sb0, logoff, m6, m7, avol1; err)] ( ( err = ESUCCESS → (∃ lpt5, log4, orphans2. disk-layout(sb0, # lpt5) ∧ sb0.main + # lpt5 = # avol1 ∧ avol1[0].mapped? ∧ is-encoded(sb0, avol1[0].data) ∧ avol1[sb0.orph].mapped? ∧ is-encoded-pad(orphans2, sb0.orphsize, avol1[sb0.orph].data) ∧ avol1[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol1[sb0.log].data = logoff) ∧ is-encoded(log4, avol1[sb0.log].data) ∧ mapped-full?(avol1, sb0.lpt, lptlebs(# lpt5, LEB_SIZE)) ∧ is-encoded(lpt5, lebs(avol1, sb0.lpt, lptlebs(# lpt5, LEB_SIZE)))) ∧ m6 = EB_PAGE_SIZE ∧ m7 = LEB_SIZE ∧ ebm-vol-inv(avol1)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0 = sb ∧ # avol1 = # avol0 ∧ adr1 = sb.indexaddr ∧ m4 = sb.maxino ∧ # lpt1 = # avol1 - sb.main ∧ is-encoded(lpt1, lebs(avol1, sb.lpt, lptlebs(# avol1 - sb.main, LEB_SIZE))) ∧ lebs(avol1, sb.lpt, lptlebs(# avol1 - sb.main, LEB_SIZE)) = lebs(avol0, sb.lpt, lptlebs(# avol1 - sb.main, LEB_SIZE)) ∧ is-encoded(log1, avol1[sb.log].data) ∧ is-encoded-pad(orphans, sb.orphsize, avol1[sb.orph].data) ∧ avol1[sb.orph] = avol0[sb.orph] ∧ avol1[sb.log] = avol0[sb.log]) → (err = ESUCCESS → avol4 = avol1) → ( err = ESUCCESS → (∃ avol. subarray(avol0, sb.main, # avol0 - sb.main) ⊆ avol ∧ ⟨adr := sb.indexaddr, m := sb.maxino; apersistence_io_recover#(; adr2, m5, ns1, log2, lpt2, adr, m, log0, lpt0, ns0, avol; err0)⟩ ( m = sb0.maxino ∧ adr = sb0.indexaddr ∧ # avol1 = sb0.main + (# avol1 - sb0.main) ∧ avol = subarray(avol1, sb0.main, # avol1 - sb0.main) ∧ is-encoded(log0, avol1[sb0.log].data) ∧ is-encoded(lpt0, lebs(avol1, sb0.lpt, lptlebs(# avol1 - sb0.main, LEB_SIZE))) ∧ is-encoded-pad(ns0, sb0.orphsize, avol1[sb0.orph].data) ∧ adr1 = adr2 ∧ m4 = m5 ∧ orphans = ns1 ∧ log1 = log2 ∧ lpt1 = lpt2 ∧ ESUCCESS = err0))) ∧ ( err ≠ ESUCCESS → (∀ adr, m, log, avol, lpt, ns. ⟨apersistence_io_recover#(; adr2, m5, ns1, log2, lpt2, adr3, m8, plog0, lpt3, ns2, avol3; err0)⟩ ( adr = adr3 ∧ m = m8 ∧ log = plog0 ∧ avol = avol3 ∧ lpt = lpt3 ∧ ns = ns2 ∧ adr1 = adr2 ∧ m4 = m5 ∧ orphans = ns1 ∧ log1 = log2 ∧ lpt1 = lpt2 ∧ err = err0))))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: superblock name: elim seq: ⊦ ( ( ( ( (adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4) subst: [sb, adr, m, m0, m1, m2, m3, m4] → [sb, adr0, m0, m2, m3, m9, m10, m11]

Additional information

Used simplifier rules: ⊦ ( ( ( ((adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4); (elim) Used terms: sb, adr0, m0, m2, m3, m9, m10, m11